Fall wk 6 – Tues.Nov.04 Welcome, roll, questions, announcements Calculus Ch.2: Concept of Derivative 2.1: How do we measure speed? 2.2: Limits 2.3: Derivative at a point VOTE today! Energy Systems, EJZ

Concept of a derivative You have already encountered derivatives. They describe the rate of change of a dependent variable (e.g. position) on an independent variable (e.g. speed) Calculus lets you describe rates of change at any point in a changing function. Your questions and key points about Ch.2 …

Example of a derivative: oil production Cumulative production vs time When is cumulative production increasing most rapidly? a, b, or c When is the production rate greatest? a, b, or c

Oil production rate = production/time When is production rate increasing most rapidly? a, b, or c When does production rate peak? a, b, or c When does production rate start to decline? a, b, or c

2.1: How do we measure speed v? vaverage= slope over an interval = Dx/Dt vinstantaneous= slope of tangent line at a point vinstantaneous = lim Dx/Dt as Dx0

2.1 continued Practice: teams do 2.1 #1-4 Discuss Ex.4 p.60 Conceptests

2.1 Finding limits algebraically Practice with Ex. 6, p.61; Teams do #5-8 Set up #17 together, finish 2.1 Conceptests

2.2: Limits Definition: lim(xc) f(x) = L Ex.1 p.63:

2.2: Limits: properties and practice Teams do Ex.3, 4, 7 (p.65-67) or #15-19

2.3: Derivative at a point

2.3: Derivative at a point: practice Teams practice with Ex.3-7; Conceptests Three ways to find the derivative=slope: Numerically (approximate) Graphically (intuitive) Analytically (exact) Compute the derivative f ’=df/dx algebraically: Ex.8 (p.75), #10-15

Calc 2 HW 1 Candidates: Ch.2.1 # 2, 4, 6, 10, 17, 18 Ch.2.2 # 2, 4, 16, 18, 20, 22 (sketch first!), 30, 36 Ch.2.3 # 6, 8, 10, 12, 14, 23, 27, 33 Due next Thus.11.Nov.04 TA Brian Orr is ill, and will not be in homeroom Wed, but will try to be in QRC at his usual times. Joey Fedrow is also available – see Help page.